-(2x-7)=(3x-5)(3x+5)

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Solution for -(2x-7)=(3x-5)(3x+5) equation: 


Simplifying
-1(2x + -7) = (3x + -5)(3x + 5)

Reorder the terms:
-1(-7 + 2x) = (3x + -5)(3x + 5)
(-7 * -1 + 2x * -1) = (3x + -5)(3x + 5)
(7 + -2x) = (3x + -5)(3x + 5)

Reorder the terms:
7 + -2x = (-5 + 3x)(3x + 5)

Reorder the terms:
7 + -2x = (-5 + 3x)(5 + 3x)

Multiply (-5 + 3x) * (5 + 3x)
7 + -2x = (-5(5 + 3x) + 3x * (5 + 3x))
7 + -2x = ((5 * -5 + 3x * -5) + 3x * (5 + 3x))
7 + -2x = ((-25 + -15x) + 3x * (5 + 3x))
7 + -2x = (-25 + -15x + (5 * 3x + 3x * 3x))
7 + -2x = (-25 + -15x + (15x + 9x2))

Combine like terms: -15x + 15x = 0
7 + -2x = (-25 + 0 + 9x2)
7 + -2x = (-25 + 9x2)

Solving
7 + -2x = -25 + 9x2

Solving for variable 'x'.

Reorder the terms:
7 + 25 + -2x + -9x2 = -25 + 9x2 + 25 + -9x2

Combine like terms: 7 + 25 = 32
32 + -2x + -9x2 = -25 + 9x2 + 25 + -9x2

Reorder the terms:
32 + -2x + -9x2 = -25 + 25 + 9x2 + -9x2

Combine like terms: -25 + 25 = 0
32 + -2x + -9x2 = 0 + 9x2 + -9x2
32 + -2x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
32 + -2x + -9x2 = 0

Factor a trinomial.
(16 + -9x)(2 + x) = 0


Subproblem 1
Set the factor '(16 + -9x)' equal to zero and attempt to solve:

Simplifying
16 + -9x = 0

Solving
16 + -9x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-16' to each side of the equation.
16 + -16 + -9x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -9x = 0 + -16
-9x = 0 + -16

Combine like terms: 0 + -16 = -16
-9x = -16

Divide each side by '-9'.
x = 1.777777778

Simplifying
x = 1.777777778

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {1.777777778, -2}

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